2. A solid cylinder of mass m, radius R, and length L falls concentrically through a vertical tube of radius R+AR, where AR <<< R. The tube is filled with gas of viscosity μ and mean free path 1. Neglect fluid forces on the front and back faces of the cylinder and consider only shear shress in annular region, assuming a linear velocity profile. Find an analytic expression for the terminal region, assuming a linear velocity profile. Find an analytic expression for the terminal velocity of fall, V, of thr cylinder (a) for no slip; (b) with slip, Su 1 (du/ dy) (Eq. 1 91). (50')